Displaying similar documents to “Eigenvalue problems of quasilinear elliptic systems on Rn.”

Extension of Díaz-Saá's inequality in R and application to a system of p-Laplacian.

Karim Chaïb (2002)

Publicacions Matemàtiques

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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...

On some nonlinear elliptic systems with coercive perturbation in R.

Said El Manouni, Abdelfattah Touzani (2003)

Revista Matemática Complutense

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A nonlinear elliptic system involving the p-Laplacian is considered in the whole R. Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.

On positive solutions of quasilinear elliptic systems

Yuanji Cheng (1997)

Czechoslovak Mathematical Journal

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In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems - Δ p u = f ( x , u , v ) , in Ω , - Δ p v = g ( x , u , v ) , in Ω , u = v = 0 , on ∂ Ω , where - Δ p is the p -Laplace operator, p > 1 and Ω is a C 1 , α -domain in ℝ n . We prove an analogue of [7, 16] for the eigenvalue problem with f ( x , u , v ) = λ 1 v p - 1 , g ( x , u , v ) = λ 2 u p - 1 and obtain a non-existence result of positive solutions for the general systems.